Does Blender resume rendering after returning from hibernation in Windows 7?
I think the best way to find out is to try it yourself ;)

Alternatives:

Something you can do to ensure your render progress is not lost is to render to an image sequence instead of directly to a video file. See the docs:


  The Direct Approach—highly not recommended and not a standard
  practice—is where you set your output format to an AVI or MOV format,
  and click [render] ANIM to render your scene directly out to a movie file.
  Blender creates one file that holds all the frames of your animation.
  You can then use Blender's VSE to add an audio track to the animation
  and render out to an MPEG format to complete your movie.
  
  The Frame Sequence is a much more stable approach, where you set your
  output format to a still format (such as JPG, PNG or MultiLayer), and
  click [render] ANIM to render your scene out to a set of images, where each
  image is the frame in the sequence.
  
  Blender creates a file for each frame of the animation. You can then
  use Blender's compositor to perform any frame manipulation (post
  processing). You can then use Blender's VSE to load that final image
  sequence, add an audio track to the animation, and render out to an
  MPEG format to complete your movie. The Frame Sequence approach is a
  little more complicated and takes more disk space, but gives you more
  flexibility.


Set start frame:

This way if the render render stops you can easily resume it by setting the Start frame to the frame after the last frame rendered and starting the render again. Whereas if you are rendering directly to a video format, there is a high probability the file will be corrupted if the render is stopped partway through. Also see the Hints section:


  Unless your animation is really simple, and you expect it to render in half an hour or less, it is always a good idea to render the animation as separate image frames in a loss-less format (TGA, PNG, BMP) rather than as a movie file from the beginning. This allows you an easy recovery if there is a problem and you have to re-start the rendering, since the frames you have already rendered will still be in the Output directory. Just change the STArt frame number to the frame number where you want to pick up from, and click ANIM again.


E.g. If the render stops while rendering frame 30, the last saved image will be frame 29. All that needs to be rendered is frame 30 up to the end, so set the Start frame to 30 and render (CtrlF12):



Disable overwrite:

Another option (as mentioned by Greg Zaal) is to disable Overwrite in Properties > Render > Output. Disabling this will skip rendering the frame if an image file corresponding to that frame already exists.

Rendering an image sequence to a video file

When the render is complete you can render the image sequence to the desired file using the VSE:


Import your image sequence with ShiftA> Image (or Header > Add > Image). This will add a new strip with your animation. Make sure it is correctly lined up with the scene start and end frames.
Set the output format to the desired location and format, then press CtrlF12. This will render the sequencer to the specified output file quite quickly, as all it is doing is encoding the already rendered images into the correct format.


Also see the workflow outlined on the docs:


  Frame Sequence Workflow
  
  
  First prepare your animation. 
  In the Dimensions panel, choose the render size, Pixel Aspect Ratio, and the Range of Frames to use, as well as the frame
  rate, which should already be set.
  In the Output panel set up your animation to be rendered out as as images, generally using a format that does not compromise any quality
  (I prefer PNG or MultiLayer because of their loss-less nature). 
  Choose the output path and file type in the Output panel as well, for example //\render\my-anim-.
  Confirm the range of your animation frame Start and End.
  Save your .blend file. 
  Press the big ''Animation'' button. Do a long task [like sleeping, playing a video game, or cleaning your driveway] while you wait for
  your computer to finish rendering the frames. 
  Once the animation is finished, use your OS file explorer to navigate into the output folder (".\render in this example). You will see lots
  of images (.png or .exr, etc... depending on the format you chose to
  render) that have a sequence number attached to them ranging from 0000
  to a max of 9999. These are your single frames. 
  In Blender, now go into the video sequence editor. 
  Choose ''Add Image'' from the add menu. Select all the frames from your output folder that you want to include in your animation (Press A
  to Select All easily). They will be added as a strip to the sequence
  editor. 
  Now you can edit the strip and add effects or simply leave it like it is. You can add other strips, like an audio strip. 
  Scrub through the animation, checking that you have included all the frames. 
  In the Scene Render buttons, in the Post Processing panel, activate Sequencer. 
  In the Format panel, choose the container and codec you want (e.g. MPEG H.264) and configure it. The video codecs are described on the
  previous page: Output Options.
  Click the ANIMATION render button and Blender will render out the sequence editor output into your movie.